4p(p-3)=8

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Solution for 4p(p-3)=8 equation: 


Simplifying
4p(p + -3) = 8

Reorder the terms:
4p(-3 + p) = 8
(-3 * 4p + p * 4p) = 8
(-12p + 4p2) = 8

Solving
-12p + 4p2 = 8

Solving for variable 'p'.

Reorder the terms:
-8 + -12p + 4p2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -12p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -3p + p2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -3p + p2)' equal to zero and attempt to solve:

Simplifying
-2 + -3p + p2 = 0

Solving
-2 + -3p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + -3p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3p + p2 = 0 + 2
-3p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3p + p2 = 2

The p term is -3p.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3p + 2.25 + p2 = 2 + 2.25

Reorder the terms:
2.25 + -3p + p2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3p + p2 = 4.25

Factor a perfect square on the left side:
(p + -1.5)(p + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(p + -1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
p + -1.5 = 2.061552813

Simplifying
p + -1.5 = 2.061552813

Reorder the terms:
-1.5 + p = 2.061552813

Solving
-1.5 + p = 2.061552813

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + p = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = 2.061552813 + 1.5
p = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
p = 3.561552813

Simplifying
p = 3.561552813


Subproblem 2
p + -1.5 = -2.061552813

Simplifying
p + -1.5 = -2.061552813

Reorder the terms:
-1.5 + p = -2.061552813

Solving
-1.5 + p = -2.061552813

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + p = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = -2.061552813 + 1.5
p = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
p = -0.561552813

Simplifying
p = -0.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.561552813, -0.561552813}
Solution
p = {3.561552813, -0.561552813}

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